A charge of #-1 C# is at the origin. How much energy would be applied to or released from a # -3 C# charge if it is moved from # ( -1, 3 ) # to #(-9 ,7 ) #?
An energy of
Electro-static Potential Energy: The electrostatic potential energy
Step 1: In this problem we have one charge (let us label it
Step 2: Now evaluate
It is not mentioned what the units of the coordinates are. So assuming them to be in meters,
So when the charge
Step 3: Both charges are negative, so the interaction between them is repulsive. For repulsive interactions the potential energy increases if the charges are brought closer together and decreases if the charges are pushed farther apart. To determine if energy has been given to or released from the system, we must know the change in potential energy. If the potential energy decreases then the system releases energy. If the potential energy increases, energy must be given to the system.
Since we saw that the potential energy increased, energy must be added to the system to displace the charge.